Stick balancing, falls and Dragon-Kings
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- Cabrera, J.L. & Milton, J.G. Eur. Phys. J. Spec. Top. (2012) 205: 231. doi:10.1140/epjst/e2012-01573-7
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The extent to which the occurrence of falls, the dominant feature of human attempts to balance a stick at their fingertip, can be predicted is examined in the context of the “Dragon-King” hypothesis. For skilled stick balancers, fluctuations in the controlled variable, namely the vertical displacement angle θ, exhibit power law behaviors. When stick balancing is made less stable by either decreasing the length of the stick or by requiring the subject to balance the stick on the surface of a table tennis racket, systematic departures from the power law behaviors are observed in the range of large θ. This observation raises the possibility that the presence of departures from the power law in the large length scale region, possibly Dragon-Kings, may identify situations in which the occurrence of a fall is more imminent. However, whether or not Dragon-Kings are observed, there is a Weibull-type survival function for stick falling. The possibility that increased risk of falling can, at least to some extent, be predicted from fluctuations in the controlled variable before the event occurs has important implications for the development of preventative strategies for the management of phenomena ranging from earthquakes to epileptic seizures to falls in the elderly.